Lay thawed pastry dough on a lightly floured board. Using a deep 3-quart casserole as a cutting guide, cut dough to shape of casserole, leaving a 1-inch overhang.
Cut a small fish shape just off-center of pastry to allow steam to escape. Brush pastry with beaten egg mixture. Transfer to a baking sheet and refrigerate.
Cook potatoes in boiling water to cover for 5 minutes, until barely tender. Drain and set aside. Also cook onions and carrots in boiling water to cover for 5 minutes. Drain and combine with potatoes.
Lightly mist a large nonstick skillet with cooking spray. Add shiitake mushrooms and sauté until mushrooms are soft, about 5 minutes.
Add garlic, and fennel; sauté until all liquid is absorbed, about 5 minutes. Stir in tomatoes with their juice, Pernod (optional), and thyme. Stir in reserved vegetable mixture.
Place half of the mushroom-vegetable mixture in the casserole. Top with fish pieces and remaining mushroom-vegetable mixture. Preheat oven to 375 degrees Farenheit.
Remove pastry from refrigerator and place over filling. Turn edges under and crimp. Bake, uncovered, for 15 to 30 minutes, until crust is golden brown and filling is bubbly. Remove from oven and let stand for 10 minutes before serving.